Stationary Stochastic Processes for Scientists and Engineers

Stochastic processes are indispensable tools for development and research in signal and image processing, automatic control, oceanography, structural reliability, environmetrics, climatology, econometrics, and many other areas of science and engineering. Suitable for a one-semester course, Stationary Stochastic Processes for Scientists and Engineers teaches students how to use these processes efficiently. Carefully balancing mathematical rigor and ease of exposition, the book provides students with a sufficient understanding of the theory and a practical appreciation of how it is used in real-life situations. Special emphasis is on the interpretation of various statistical models and concepts as well as the types of questions statistical analysis can answer. The text first introduces numerous examples from signal processing, economics, and general natural sciences and technology. It then covers the estimation of mean value and covariance functions, properties of stationary Poisson processes, Fourier analysis of the covariance function (spectral analysis), and the Gaussian distribution.
The book also focuses on input-output relations in linear filters, describes discrete-time auto-regressive and moving average processes, and explains how to solve linear stochastic differential equations. It concludes with frequency analysis and estimation of spectral densities. With a focus on model building and interpreting the statistical concepts, this classroom-tested book conveys a broad understanding of the mechanisms that generate stationary stochastic processes. By combining theory and applications, the text gives students a well-rounded introduction to these processes. To enable hands-on practice, MATLAB(R) code is available online.

Stochastic Processes Some stochastic models Definition of a stochastic process Distribution functions Stationary Processes Introduction Moment functions Stationary processes Random phase and amplitude Estimation of mean value and covariance functionStationary processes and the non-stationary reality Monte Carlo simulation from covariance function The Poisson Process and Its Relatives Introduction The Poisson process Stationary independent increments The covariance intensity function Spatial Poisson process Inhomogeneous Poisson process Monte Carlo simulation of Poisson processes Spectral Representations Introduction Spectrum in continuous time Spectrum in discrete timeSampling and the aliasing effect A few more remarks and difficultiesMonte Carlo simulation from spectrum Gaussian Processes IntroductionGaussian processes The Wiener process Relatives of the Gaussian process The Lévy process and shot noise process Simulation of Gaussian process from spectrum Linear Filters—General Theory Introduction Linear systems and linear filtersContinuity, differentiation, integration White noise in continuous time Cross-covariance and cross-spectrum AR, MA, and ARMA Models Introduction Auto-regression and moving average Estimation of AR parameters Prediction in AR and ARMA modelsA simple non-linear model—the GARCH process Monte Carlo simulation of ARMA processes Linear Filters—Applications Introduction Differential equations with random input The envelope Matched filter Wiener filter Kalman filterAn example from structural dynamicsMonte Carlo simulation in continuous time Frequency Analysis and Spectral Estimation Introduction The periodogramThe discrete Fourier transform and the FFT Bias reduction—data windowingReduction of variance Appendix A: Some Probability and Statistics Appendix B: Delta Functions and Stieltjes IntegralsAppendix C: Kolmogorov’s Existence Theorem Appendix D: Covariance/Spectral Density Pairs Appendix E: A Historical Background References Index Exercises appear at the end of each chapter.